Using the steps below, you are going to show that in the Hotelling model the optimal configura- tion of firms (from the benevolent social planner's/technocrat's perspective) is at a = 1, b = 14. 3 1. What is the total surplus (consumer surplus + producer surplus) generated by a purchase from consumer x at firm A? firm B? 2. Using what you found in 1, show that is socially optimal (total surplus is maximized) for x to purchase from A if t. (a-x)2 t (1-b - x). = 3. Assume a symmetric equilibrium where a b. Part 2 shows that is socially optimal for consumer x to purchase from the store that minimizes his individual travel costs. Likewise, the social planner would like to choose a that minimizes city-wide travel costs. Use inte- gration to find the total travel costs over all x. (Hint: It is save to assume that a stays in the interval [0,2]) 4. Show that the a that minimizes the total travel costs is a = 5. Discuss how the free market generates "too much" product differentiation in the Hotelling model.